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vesna_86 [32]
3 years ago
6

Which of the following are roots of the polynomial function? Check all that apply f(x) = x^3 + 3x^2 - 9x + 5

Mathematics
1 answer:
lakkis [162]3 years ago
8 0

Answer:

x = 1 or x = -5

Step-by-step explanation:

Solve for x:

x^3 + 3 x^2 - 9 x + 5 = 0

The left hand side factors into a product with two terms:

(x - 1)^2 (x + 5) = 0

Split into two equations:

(x - 1)^2 = 0 or x + 5 = 0

Take the square root of both sides:

x - 1 = 0 or x + 5 = 0

Add 1 to both sides:

x = 1 or x + 5 = 0

Subtract 5 from both sides:

Answer:  x = 1 or x = -5

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5. Brianna earns $19,500 per year. Lisa earns $1,000 per month. Write a numerical expression that represents how much more Brian
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Answer:

19,500 - (1,000 x 12) = X

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3 years ago
Find the exact values of sin2 θ for cos θ = 3/18 on the interval 0° ≤ θ ≤ 90°
mote1985 [20]

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sin(2\theta)=\frac{\sqrt{35} }{18}

Step-by-step explanation:

Recall the formula for the sine of the double angle:

sin(2\theta)=2*sin(\theta)*cos(\theta)

we know that cos(\theta)=\frac{3}{18}, and that \theta is in the interval between 0 and 90 degrees, where both the functions sine and cosine are non-negative numbers. Based on such, we can find using the Pythagorean trigonometric property that relates sine and cosine of the same angle, what sin(\theta) is:

cos^2(\theta)+sin^2(\theta)=1\\sin^2(\theta)=1-cos^2(\theta)\\sin(\theta)=\sqrt{1-cos^2(\theta)} \\sin(\theta)=\sqrt{1-(\frac{3}{18} )^2}\\sin(\theta)=\sqrt{1-\frac{9}{324} }\\sin(\theta)=\sqrt{\frac{324-9}{324} }\\sin(\theta)=\sqrt{\frac{315}{324} }\\\\sin(\theta)=\frac{3}{18}\sqrt{35 }

With this information, we can now complete the value of the sine of the double angle requested:

sin(2\theta)=2*sin(\theta)*cos(\theta)\\sin(2\theta)=2*\frac{3}{18} \,\sqrt{35} \,\frac{3}{18}\\sin(2\theta)=\frac{2*3*3}{18*18}\,\sqrt{35} \\sin(2\theta)=\frac{\sqrt{35} }{18}

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